The Equivalent Circuit Analysis of The Solar Cell

Figure 2.4 The diagram of solar cell equivalent circuit.

Figure 2.4 illustrates the equivalent circuit of solar cell. From this diagram, one could find the photo-generated current (I) as follows [11]:

(2-1) where I_sc is the short-circuit current (also called light-generated current, I_L), I₀ is the reverse saturation current of the diode, k is the Boltzmann‘s constant, T is the absolute temperature in degrees Kelvin, n is the ideality factor of diode (1＜n＜2, n=1 for the Shockley equation), R_s is the equivalent series resistance and Rsh is the equivalent shunt resistance of the solar cell.

An idealized solar cell, the series resistance R_s is close to infinity and treats as open in the equivalent circuit. Therefore, the Eq. (2-1) can simplified as:

(2-2) In Figure 2.4, when the intensity of solar radiation is weak, the current of diode is approximately the leakage current (

), therefore, Rs can be ignore and Rsh effect is important, then Eq. (2-1) can be rewritten as:

(2-3)

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When the intensity of solar radiation is great, the light-generated current is great and diode is on condition. Therefore, the current of diode is greater than the leakage current (

), and the Rsh can be ignore and the Rs effect is important. Then the Eq. (2-1) can be rewritten as:

(2-4)

Figure 2.5 The I-V characteristics with and without illumination.

The I-V characteristics of solar cell in dark condition and under illumination were shown in Figure 2.5 [12]. Four parameters are usually used to characterize the solar cell output performances and shown in this figure. The parameters used to describe the solar cell performances are indicated as follows [13]:

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(1) Short-Circuit Current, Isc

I_sc is determined on the voltage (V) equal to zero by Eq. (2-2). This is equal to the light-generated current IL ideally. As V=0, the Eq. (2-2) can be written as:

(2-5) (2) Open-Circuit Voltage, Voc

The open-circuit voltage V_oc can be solved in I=0 and V=V_oc from Eq. (2-2), which is expressed as:

(2-6)

V_oc is determined by the properties of the semiconductor by virtue of its dependence on I0.

(3) Fill Factor, FF

Which is defined as the maximum ratio of the output power to the product on the short-circuit current and open-circuit voltage, which can be expressed as:

(2-7) It is measure of how squareness the output characteristics are. For cell of reasonably efficiency, it has a value in the range 0.7 to 0.85.

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(4) Conversion Efficiency, η

The conversion efficiency of solar cell is defined as the maximum ratio of the output power to the input power, which can be expressed as

where Pin is the total power under the light incident to the cell.

The solar cell parameters such as open-circuit voltage Voc, short-circuit current Isc and fill factor FF can provide the information about designing and improving the photodiode due to their characteristics depended on the properties of the semiconductor materials and the structure of device.

(5) Quantum Efficiency

Quantum efficiency (QE) is the ratio of the number of charge carriers collected by the solar cell to the number of photons of a given energy shining on the solar cell. QE therefore relates to the response of a solar cell to the various wavelengths in the spectrum of light shining on the cell. The QE is given as a function of either wavelength or energy. If all the photons of a certain wavelength are absorbed and we collect the resulting minority carriers (for example, electrons in a p-type material), and then the QE at that particular wavelength has a value of one. The QE for photons with energy below the bandgap is zero.

The quantum efficiency ideally has a square shape, where the QE value is fairly constant across the entire spectrum of wavelengths measured. However, the QE for most solar cells is reduced because of the effects of recombination, where charge carriers are not able to move into an external circuit. The same mechanisms that affect the collection probability also affect the QE. For example, modifying the front surface can affect carriers generated near the surface. And because high-energy (blue) light is absorbed very close to the surface,

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considerable recombination at the front surface will affect the "blue" portion of the QE.

Similarly, lower energy (green) light is absorbed in the bulk of a solar cell, and a low diffusion length will affect the collection probability from the solar cell bulk, reducing the QE in the green portion of the spectrum. In somewhat technical terms, the quantum efficiency can be viewed as the collection probability due to the generation profile of a single wavelength, integrated over the device thickness and normalized to the number of incident photons.

"Quantum efficiency" is also sometimes called IPCE, which stands for Incident-Photon-to-electron Conversion Efficiency.

Two types of quantum efficiency (QE) of a solar cell are often considered:

 External Quantum Efficiency (EQE) is the ratio of the number of charge carriers collected by the solar cell to the number of photons of a given energy shining on the solar cell from outside (incident photons).

 Internal Quantum Efficiency (IQE) is the ratio of the number of charge carriers collected by the solar cell to the number of photons of a given energy that shine on the solar cell from outside and are absorbed by the cell.

The IQE is always larger than the EQE. A low IQE indicates that the active layer of the solar cell is unable to make good use of the photons. A low EQE can indicate that, but it can also, instead, indicate that a lot of the light was reflected.

To measure the IQE, one first measures the EQE of the solar device, then measures its transmission and reflection, and combines these data to infer the IQE.

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(6) Parasitic Resistances

In real cells power is dissipated through the resistance of the contacts and through leakage currents around the sides of the device. These effects are equivalent electrically to two parasitic resistances in series (Rs) and in parallel (Rsh) with the cell (Figure 2.4).

The series resistance arises from the resistance of the cell material to current flow, particularly through the front surface to the contacts, and from resistive contacts. Series resistance is a particular problem at high current densities, for instance under concentrated light. The parallel or shunt resistance arise from leakage of current through the cell, around the edges of the device and between contacts of different polarity. It is a problem in poorly rectifying devices.

Series and parallel resistance reduce the fill factor as shown in Figure 2.6. For an efficient cell we want R_s to be as small and R_sh to be as large as possible.

Figure 2.6 Effect of increasing series and reducing parallel resistances. In each case the outer curve has Rs = 0 and Rsh = ∞. In each case the effect of the resistances is to reduce the area of the maximum power rectangle compared to Jsc × Voc.

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